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of 32
pro vyhledávání: '"Islam, Mitul"'
We consider rigidity properties of compact symmetric spaces $X$ with metric $g_0$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $\kappa$ bounded by $0 \leq \kappa \leq 1$. If $g$ equals $g_0$ outside a convex p
Externí odkaz:
http://arxiv.org/abs/2406.00558
Autor:
Islam, Mitul, Weisman, Theodore
We study properties of "hyperbolic directions" in groups acting cocompactly on properly convex domains in real projective space, from three different perspectives simultaneously: the (coarse) metric geometry of the Hilbert metric, the projective geom
Externí odkaz:
http://arxiv.org/abs/2405.03269
We consider actions of cocompact lattices in semisimple Lie groups of the noncompact type on their boundaries $G/Q$, $Q$ a parabolic group, the so-called standard actions. We show that perturbations of the standard action in the homeomorphism group c
Externí odkaz:
http://arxiv.org/abs/2303.00543
Autor:
Islam, Mitul, Zimmer, Andrew
In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a characterization of su
Externí odkaz:
http://arxiv.org/abs/2203.16596
Autor:
Islam, Mitul, Zimmer, Andrew
In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face in the ide
Externí odkaz:
http://arxiv.org/abs/2104.05056
Autor:
Islam, Mitul, Zimmer, Andrew
A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the
Externí odkaz:
http://arxiv.org/abs/2009.05191
Autor:
Islam, Mitul
We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for Hilbert ge
Externí odkaz:
http://arxiv.org/abs/1912.13013
Autor:
Islam, Mitul, Zimmer, Andrew
Publikováno v:
Geom. Topol. 27 (2023) 417-511
In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be relatively h
Externí odkaz:
http://arxiv.org/abs/1910.08885
Autor:
Islam, Mitul, Zimmer, Andrew
In this paper, we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish an analogue of the well known flat torus theorem for ${\rm CAT}(0)$
Externí odkaz:
http://arxiv.org/abs/1907.03277
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